[Blueduck01]

if an elastic band is influenced by a positive force f, the polymers adjust according to the function f.
The differential of the internal energy of an elastic band with the length L can be written as dU = Tds + fdL
By the folowing function you can obtain all the thermodynamic functions, such as the Helmholtz free energy:
dA = -Sdt + fdL

it is assumed that the relation between f and L is given by f = k(L-L₀)
where L₀ is the length of the rubber band while not being subjected to any force f, and k being a positive constant. It is furthermore assumed that (δU/δL)_T = 0.

Consider the experiment of having a weight attached to a rubber band at temperature T₁ with length L₁ . The temperature is raised to T₂ and the length is now L₂.

Problem: By using the general relation (δL/δT)_f = -(δL/δf)_T * (δf/δT)_L
show the relation (L₂-L₀) / (L₁-L₀) = T₁/T₂